Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [11,13,Mod(10,11)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(11, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 13, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("11.10");
S:= CuspForms(chi, 13);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 11 \) |
Weight: | \( k \) | \(=\) | \( 13 \) |
Character orbit: | \([\chi]\) | \(=\) | 11.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.0539319900\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 30654x^{8} + 318945120x^{6} + 1305642637440x^{4} + 2049564619929600x^{2} + 957721368231936000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{3}\cdot 11^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 10.1 | ||
Root | \(-110.069i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 11.10 |
Dual form | 11.13.b.b.10.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/11\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 110.069i | − | 1.71983i | −0.510438 | − | 0.859915i | \(-0.670517\pi\) | ||
0.510438 | − | 0.859915i | \(-0.329483\pi\) | |||||||
\(3\) | 1258.46 | 1.72629 | 0.863143 | − | 0.504959i | \(-0.168493\pi\) | ||||
0.863143 | + | 0.504959i | \(0.168493\pi\) | |||||||
\(4\) | −8019.20 | −1.95781 | ||||||||
\(5\) | 14011.2 | 0.896718 | 0.448359 | − | 0.893854i | \(-0.352009\pi\) | ||||
0.448359 | + | 0.893854i | \(0.352009\pi\) | |||||||
\(6\) | − | 138518.i | − | 2.96892i | ||||||
\(7\) | − | 131085.i | − | 1.11420i | −0.830444 | − | 0.557102i | \(-0.811913\pi\) | ||
0.830444 | − | 0.557102i | \(-0.188087\pi\) | |||||||
\(8\) | 431823.i | 1.64727i | ||||||||
\(9\) | 1.05229e6 | 1.98006 | ||||||||
\(10\) | − | 1.54220e6i | − | 1.54220i | ||||||
\(11\) | −1.39887e6 | + | 1.08701e6i | −0.789627 | + | 0.613587i | ||||
\(12\) | −1.00919e7 | −3.37974 | ||||||||
\(13\) | − | 3.22288e6i | − | 0.667704i | −0.942625 | − | 0.333852i | \(-0.891651\pi\) | ||
0.942625 | − | 0.333852i | \(-0.108349\pi\) | |||||||
\(14\) | −1.44284e7 | −1.91624 | ||||||||
\(15\) | 1.76326e7 | 1.54799 | ||||||||
\(16\) | 1.46837e7 | 0.875216 | ||||||||
\(17\) | 3.44290e7i | 1.42637i | 0.700978 | + | 0.713183i | \(0.252747\pi\) | ||||
−0.700978 | + | 0.713183i | \(0.747253\pi\) | |||||||
\(18\) | − | 1.15824e8i | − | 3.40537i | ||||||
\(19\) | 3.46006e7i | 0.735465i | 0.929932 | + | 0.367733i | \(0.119866\pi\) | ||||
−0.929932 | + | 0.367733i | \(0.880134\pi\) | |||||||
\(20\) | −1.12359e8 | −1.75561 | ||||||||
\(21\) | − | 1.64965e8i | − | 1.92343i | ||||||
\(22\) | 1.19646e8 | + | 1.53973e8i | 1.05526 | + | 1.35802i | ||||
\(23\) | 1.65999e8 | 1.12134 | 0.560672 | − | 0.828038i | \(-0.310543\pi\) | ||||
0.560672 | + | 0.828038i | \(0.310543\pi\) | |||||||
\(24\) | 5.43433e8i | 2.84366i | ||||||||
\(25\) | −4.78263e7 | −0.195897 | ||||||||
\(26\) | −3.54740e8 | −1.14834 | ||||||||
\(27\) | 6.55465e8 | 1.69187 | ||||||||
\(28\) | 1.05120e9i | 2.18140i | ||||||||
\(29\) | − | 9.11924e8i | − | 1.53310i | −0.642184 | − | 0.766551i | \(-0.721971\pi\) | ||
0.642184 | − | 0.766551i | \(-0.278029\pi\) | |||||||
\(30\) | − | 1.94080e9i | − | 2.66228i | ||||||
\(31\) | 2.56746e8 | 0.289290 | 0.144645 | − | 0.989484i | \(-0.453796\pi\) | ||||
0.144645 | + | 0.989484i | \(0.453796\pi\) | |||||||
\(32\) | 1.52526e8i | 0.142051i | ||||||||
\(33\) | −1.76043e9 | + | 1.36796e9i | −1.36312 | + | 1.05923i | ||||
\(34\) | 3.78957e9 | 2.45311 | ||||||||
\(35\) | − | 1.83666e9i | − | 0.999126i | ||||||
\(36\) | −8.43850e9 | −3.87659 | ||||||||
\(37\) | 1.07127e9 | 0.417532 | 0.208766 | − | 0.977966i | \(-0.433055\pi\) | ||||
0.208766 | + | 0.977966i | \(0.433055\pi\) | |||||||
\(38\) | 3.80846e9 | 1.26487 | ||||||||
\(39\) | − | 4.05588e9i | − | 1.15265i | ||||||
\(40\) | 6.05036e9i | 1.47714i | ||||||||
\(41\) | 5.70065e9i | 1.20011i | 0.799959 | + | 0.600055i | \(0.204855\pi\) | ||||
−0.799959 | + | 0.600055i | \(0.795145\pi\) | |||||||
\(42\) | −1.81576e10 | −3.30798 | ||||||||
\(43\) | 3.44514e9i | 0.544999i | 0.962156 | + | 0.272500i | \(0.0878504\pi\) | ||||
−0.962156 | + | 0.272500i | \(0.912150\pi\) | |||||||
\(44\) | 1.12178e10 | − | 8.71692e9i | 1.54594 | − | 1.20129i | ||||
\(45\) | 1.47438e10 | 1.77556 | ||||||||
\(46\) | − | 1.82714e10i | − | 1.92852i | ||||||
\(47\) | −2.28345e9 | −0.211839 | −0.105919 | − | 0.994375i | \(-0.533779\pi\) | ||||
−0.105919 | + | 0.994375i | \(0.533779\pi\) | |||||||
\(48\) | 1.84789e10 | 1.51087 | ||||||||
\(49\) | −3.34197e9 | −0.241449 | ||||||||
\(50\) | 5.26420e9i | 0.336909i | ||||||||
\(51\) | 4.33276e10i | 2.46232i | ||||||||
\(52\) | 2.58449e10i | 1.30724i | ||||||||
\(53\) | 6.37380e9 | 0.287570 | 0.143785 | − | 0.989609i | \(-0.454073\pi\) | ||||
0.143785 | + | 0.989609i | \(0.454073\pi\) | |||||||
\(54\) | − | 7.21465e10i | − | 2.90973i | ||||||
\(55\) | −1.95999e10 | + | 1.52303e10i | −0.708073 | + | 0.550215i | ||||
\(56\) | 5.66054e10 | 1.83540 | ||||||||
\(57\) | 4.35436e10i | 1.26962i | ||||||||
\(58\) | −1.00375e11 | −2.63667 | ||||||||
\(59\) | 4.47524e10 | 1.06097 | 0.530487 | − | 0.847693i | \(-0.322009\pi\) | ||||
0.530487 | + | 0.847693i | \(0.322009\pi\) | |||||||
\(60\) | −1.41399e11 | −3.03068 | ||||||||
\(61\) | − | 2.20652e9i | − | 0.0428281i | −0.999771 | − | 0.0214141i | \(-0.993183\pi\) | ||
0.999771 | − | 0.0214141i | \(-0.00681683\pi\) | |||||||
\(62\) | − | 2.82598e10i | − | 0.497530i | ||||||
\(63\) | − | 1.37939e11i | − | 2.20619i | ||||||
\(64\) | 7.69328e10 | 1.11952 | ||||||||
\(65\) | − | 4.51565e10i | − | 0.598743i | ||||||
\(66\) | 1.50570e11 | + | 1.93769e11i | 1.82169 | + | 2.34434i | ||||
\(67\) | −3.46978e10 | −0.383578 | −0.191789 | − | 0.981436i | \(-0.561429\pi\) | ||||
−0.191789 | + | 0.981436i | \(0.561429\pi\) | |||||||
\(68\) | − | 2.76093e11i | − | 2.79256i | ||||||
\(69\) | 2.08904e11 | 1.93576 | ||||||||
\(70\) | −2.02159e11 | −1.71833 | ||||||||
\(71\) | −1.37060e11 | −1.06995 | −0.534973 | − | 0.844869i | \(-0.679678\pi\) | ||||
−0.534973 | + | 0.844869i | \(0.679678\pi\) | |||||||
\(72\) | 4.54402e11i | 3.26171i | ||||||||
\(73\) | 6.76442e10i | 0.446986i | 0.974706 | + | 0.223493i | \(0.0717459\pi\) | ||||
−0.974706 | + | 0.223493i | \(0.928254\pi\) | |||||||
\(74\) | − | 1.17914e11i | − | 0.718083i | ||||||
\(75\) | −6.01877e10 | −0.338174 | ||||||||
\(76\) | − | 2.77469e11i | − | 1.43990i | ||||||
\(77\) | 1.42490e11 | + | 1.83371e11i | 0.683661 | + | 0.879805i | ||||
\(78\) | −4.46426e11 | −1.98236 | ||||||||
\(79\) | 9.62506e10i | 0.395951i | 0.980207 | + | 0.197975i | \(0.0634366\pi\) | ||||
−0.980207 | + | 0.197975i | \(0.936563\pi\) | |||||||
\(80\) | 2.05736e11 | 0.784822 | ||||||||
\(81\) | 2.65650e11 | 0.940589 | ||||||||
\(82\) | 6.27465e11 | 2.06398 | ||||||||
\(83\) | − | 3.17921e11i | − | 0.972413i | −0.873844 | − | 0.486207i | \(-0.838380\pi\) | ||
0.873844 | − | 0.486207i | \(-0.161620\pi\) | |||||||
\(84\) | 1.32289e12i | 3.76572i | ||||||||
\(85\) | 4.82392e11i | 1.27905i | ||||||||
\(86\) | 3.79203e11 | 0.937306 | ||||||||
\(87\) | − | 1.14762e12i | − | 2.64657i | ||||||
\(88\) | −4.69394e11 | − | 6.04065e11i | −1.01075 | − | 1.30073i | ||||
\(89\) | 1.40561e11 | 0.282829 | 0.141415 | − | 0.989950i | \(-0.454835\pi\) | ||||
0.141415 | + | 0.989950i | \(0.454835\pi\) | |||||||
\(90\) | − | 1.62284e12i | − | 3.05366i | ||||||
\(91\) | −4.22471e11 | −0.743958 | ||||||||
\(92\) | −1.33118e12 | −2.19538 | ||||||||
\(93\) | 3.23105e11 | 0.499398 | ||||||||
\(94\) | 2.51338e11i | 0.364326i | ||||||||
\(95\) | 4.84797e11i | 0.659505i | ||||||||
\(96\) | 1.91948e11i | 0.245221i | ||||||||
\(97\) | −1.24384e12 | −1.49326 | −0.746630 | − | 0.665239i | \(-0.768329\pi\) | ||||
−0.746630 | + | 0.665239i | \(0.768329\pi\) | |||||||
\(98\) | 3.67847e11i | 0.415251i | ||||||||
\(99\) | −1.47202e12 | + | 1.14384e12i | −1.56351 | + | 1.21494i | ||||
\(100\) | 3.83529e11 | 0.383529 | ||||||||
\(101\) | 1.66474e12i | 1.56826i | 0.620597 | + | 0.784129i | \(0.286890\pi\) | ||||
−0.620597 | + | 0.784129i | \(0.713110\pi\) | |||||||
\(102\) | 4.76903e12 | 4.23476 | ||||||||
\(103\) | −1.06069e12 | −0.888310 | −0.444155 | − | 0.895950i | \(-0.646496\pi\) | ||||
−0.444155 | + | 0.895950i | \(0.646496\pi\) | |||||||
\(104\) | 1.39171e12 | 1.09989 | ||||||||
\(105\) | − | 2.31137e12i | − | 1.72478i | ||||||
\(106\) | − | 7.01558e11i | − | 0.494570i | ||||||
\(107\) | − | 5.47656e11i | − | 0.364926i | −0.983213 | − | 0.182463i | \(-0.941593\pi\) | ||
0.983213 | − | 0.182463i | \(-0.0584070\pi\) | |||||||
\(108\) | −5.25631e12 | −3.31237 | ||||||||
\(109\) | − | 1.30910e12i | − | 0.780572i | −0.920694 | − | 0.390286i | \(-0.872376\pi\) | ||
0.920694 | − | 0.390286i | \(-0.127624\pi\) | |||||||
\(110\) | 1.67638e12 | + | 2.15734e12i | 0.946275 | + | 1.21776i | ||||
\(111\) | 1.34816e12 | 0.720779 | ||||||||
\(112\) | − | 1.92481e12i | − | 0.975169i | ||||||
\(113\) | −2.96485e12 | −1.42407 | −0.712036 | − | 0.702143i | \(-0.752227\pi\) | ||||
−0.712036 | + | 0.702143i | \(0.752227\pi\) | |||||||
\(114\) | 4.79280e12 | 2.18354 | ||||||||
\(115\) | 2.32585e12 | 1.00553 | ||||||||
\(116\) | 7.31290e12i | 3.00152i | ||||||||
\(117\) | − | 3.39140e12i | − | 1.32210i | ||||||
\(118\) | − | 4.92586e12i | − | 1.82469i | ||||||
\(119\) | 4.51312e12 | 1.58926 | ||||||||
\(120\) | 7.61416e12i | 2.54997i | ||||||||
\(121\) | 7.75260e11 | − | 3.04117e12i | 0.247022 | − | 0.969010i | ||||
\(122\) | −2.42870e11 | −0.0736571 | ||||||||
\(123\) | 7.17405e12i | 2.07173i | ||||||||
\(124\) | −2.05890e12 | −0.566376 | ||||||||
\(125\) | −4.09081e12 | −1.07238 | ||||||||
\(126\) | −1.51828e13 | −3.79428 | ||||||||
\(127\) | 3.01347e11i | 0.0718198i | 0.999355 | + | 0.0359099i | \(0.0114329\pi\) | ||||
−0.999355 | + | 0.0359099i | \(0.988567\pi\) | |||||||
\(128\) | − | 7.84317e12i | − | 1.78333i | ||||||
\(129\) | 4.33558e12i | 0.940825i | ||||||||
\(130\) | −4.97033e12 | −1.02973 | ||||||||
\(131\) | − | 4.66258e12i | − | 0.922568i | −0.887253 | − | 0.461284i | \(-0.847389\pi\) | ||
0.887253 | − | 0.461284i | \(-0.152611\pi\) | |||||||
\(132\) | 1.41172e13 | − | 1.09699e13i | 2.66874 | − | 2.07377i | ||||
\(133\) | 4.53562e12 | 0.819458 | ||||||||
\(134\) | 3.81916e12i | 0.659688i | ||||||||
\(135\) | 9.18387e12 | 1.51713 | ||||||||
\(136\) | −1.48672e13 | −2.34961 | ||||||||
\(137\) | −1.97840e12 | −0.299220 | −0.149610 | − | 0.988745i | \(-0.547802\pi\) | ||||
−0.149610 | + | 0.988745i | \(0.547802\pi\) | |||||||
\(138\) | − | 2.29938e13i | − | 3.32918i | ||||||
\(139\) | 2.42384e12i | 0.336058i | 0.985782 | + | 0.168029i | \(0.0537403\pi\) | ||||
−0.985782 | + | 0.168029i | \(0.946260\pi\) | |||||||
\(140\) | 1.47285e13i | 1.95610i | ||||||||
\(141\) | −2.87364e12 | −0.365694 | ||||||||
\(142\) | 1.50861e13i | 1.84012i | ||||||||
\(143\) | 3.50329e12 | + | 4.50840e12i | 0.409695 | + | 0.527237i | ||||
\(144\) | 1.54515e13 | 1.73298 | ||||||||
\(145\) | − | 1.27772e13i | − | 1.37476i | ||||||
\(146\) | 7.44554e12 | 0.768739 | ||||||||
\(147\) | −4.20574e12 | −0.416810 | ||||||||
\(148\) | −8.59074e12 | −0.817448 | ||||||||
\(149\) | − | 8.27011e12i | − | 0.755777i | −0.925851 | − | 0.377888i | \(-0.876650\pi\) | ||
0.925851 | − | 0.377888i | \(-0.123350\pi\) | |||||||
\(150\) | 6.62480e12i | 0.581601i | ||||||||
\(151\) | 4.62597e12i | 0.390248i | 0.980779 | + | 0.195124i | \(0.0625110\pi\) | ||||
−0.980779 | + | 0.195124i | \(0.937489\pi\) | |||||||
\(152\) | −1.49413e13 | −1.21151 | ||||||||
\(153\) | 3.62292e13i | 2.82430i | ||||||||
\(154\) | 2.01835e13 | − | 1.56838e13i | 1.51311 | − | 1.17578i | ||||
\(155\) | 3.59733e12 | 0.259412 | ||||||||
\(156\) | 3.25249e13i | 2.25667i | ||||||||
\(157\) | −2.00659e13 | −1.33987 | −0.669933 | − | 0.742421i | \(-0.733677\pi\) | ||||
−0.669933 | + | 0.742421i | \(0.733677\pi\) | |||||||
\(158\) | 1.05942e13 | 0.680967 | ||||||||
\(159\) | 8.02118e12 | 0.496427 | ||||||||
\(160\) | 2.13708e12i | 0.127380i | ||||||||
\(161\) | − | 2.17600e13i | − | 1.24940i | ||||||
\(162\) | − | 2.92399e13i | − | 1.61765i | ||||||
\(163\) | −2.42763e12 | −0.129437 | −0.0647184 | − | 0.997904i | \(-0.520615\pi\) | ||||
−0.0647184 | + | 0.997904i | \(0.520615\pi\) | |||||||
\(164\) | − | 4.57146e13i | − | 2.34959i | ||||||
\(165\) | −2.46658e13 | + | 1.91668e13i | −1.22234 | + | 0.949828i | ||||
\(166\) | −3.49933e13 | −1.67238 | ||||||||
\(167\) | 4.96523e12i | 0.228897i | 0.993429 | + | 0.114449i | \(0.0365102\pi\) | ||||
−0.993429 | + | 0.114449i | \(0.963490\pi\) | |||||||
\(168\) | 7.12358e13 | 3.16842 | ||||||||
\(169\) | 1.29111e13 | 0.554171 | ||||||||
\(170\) | 5.30965e13 | 2.19974 | ||||||||
\(171\) | 3.64098e13i | 1.45627i | ||||||||
\(172\) | − | 2.76273e13i | − | 1.06701i | ||||||
\(173\) | − | 3.59785e13i | − | 1.34204i | −0.741438 | − | 0.671022i | \(-0.765856\pi\) | ||
0.741438 | − | 0.671022i | \(-0.234144\pi\) | |||||||
\(174\) | −1.26318e14 | −4.55165 | ||||||||
\(175\) | 6.26931e12i | 0.218269i | ||||||||
\(176\) | −2.05406e13 | + | 1.59613e13i | −0.691094 | + | 0.537021i | ||||
\(177\) | 5.63193e13 | 1.83154 | ||||||||
\(178\) | − | 1.54714e13i | − | 0.486418i | ||||||
\(179\) | 5.45793e13 | 1.65924 | 0.829621 | − | 0.558326i | \(-0.188556\pi\) | ||||
0.829621 | + | 0.558326i | \(0.188556\pi\) | |||||||
\(180\) | −1.18234e14 | −3.47621 | ||||||||
\(181\) | −2.92102e13 | −0.830736 | −0.415368 | − | 0.909653i | \(-0.636347\pi\) | ||||
−0.415368 | + | 0.909653i | \(0.636347\pi\) | |||||||
\(182\) | 4.65010e13i | 1.27948i | ||||||||
\(183\) | − | 2.77682e12i | − | 0.0739336i | ||||||
\(184\) | 7.16822e13i | 1.84716i | ||||||||
\(185\) | 1.50098e13 | 0.374408 | ||||||||
\(186\) | − | 3.55639e13i | − | 0.858879i | ||||||
\(187\) | −3.74246e13 | − | 4.81618e13i | −0.875200 | − | 1.12630i | ||||
\(188\) | 1.83115e13 | 0.414740 | ||||||||
\(189\) | − | 8.59216e13i | − | 1.88509i | ||||||
\(190\) | 5.33611e13 | 1.13424 | ||||||||
\(191\) | −4.78497e13 | −0.985550 | −0.492775 | − | 0.870157i | \(-0.664017\pi\) | ||||
−0.492775 | + | 0.870157i | \(0.664017\pi\) | |||||||
\(192\) | 9.68170e13 | 1.93261 | ||||||||
\(193\) | 1.00158e14i | 1.93794i | 0.247170 | + | 0.968972i | \(0.420499\pi\) | ||||
−0.247170 | + | 0.968972i | \(0.579501\pi\) | |||||||
\(194\) | 1.36909e14i | 2.56815i | ||||||||
\(195\) | − | 5.68278e13i | − | 1.03360i | ||||||
\(196\) | 2.67999e13 | 0.472712 | ||||||||
\(197\) | − | 9.24406e13i | − | 1.58149i | −0.612148 | − | 0.790743i | \(-0.709694\pi\) | ||
0.612148 | − | 0.790743i | \(-0.290306\pi\) | |||||||
\(198\) | 1.25902e14 | + | 1.62023e14i | 2.08949 | + | 2.68897i | ||||
\(199\) | −7.64734e12 | −0.123138 | −0.0615690 | − | 0.998103i | \(-0.519610\pi\) | ||||
−0.0615690 | + | 0.998103i | \(0.519610\pi\) | |||||||
\(200\) | − | 2.06525e13i | − | 0.322695i | ||||||
\(201\) | −4.36659e13 | −0.662165 | ||||||||
\(202\) | 1.83236e14 | 2.69714 | ||||||||
\(203\) | −1.19540e14 | −1.70819 | ||||||||
\(204\) | − | 3.47453e14i | − | 4.82075i | ||||||
\(205\) | 7.98730e13i | 1.07616i | ||||||||
\(206\) | 1.16749e14i | 1.52774i | ||||||||
\(207\) | 1.74679e14 | 2.22033 | ||||||||
\(208\) | − | 4.73238e13i | − | 0.584386i | ||||||
\(209\) | −3.76111e13 | − | 4.84019e13i | −0.451272 | − | 0.580743i | ||||
\(210\) | −2.54410e14 | −2.96632 | ||||||||
\(211\) | 7.34913e12i | 0.0832801i | 0.999133 | + | 0.0416400i | \(0.0132583\pi\) | ||||
−0.999133 | + | 0.0416400i | \(0.986742\pi\) | |||||||
\(212\) | −5.11127e13 | −0.563007 | ||||||||
\(213\) | −1.72485e14 | −1.84703 | ||||||||
\(214\) | −6.02799e13 | −0.627610 | ||||||||
\(215\) | 4.82706e13i | 0.488711i | ||||||||
\(216\) | 2.83045e14i | 2.78697i | ||||||||
\(217\) | − | 3.36555e13i | − | 0.322328i | ||||||
\(218\) | −1.44091e14 | −1.34245 | ||||||||
\(219\) | 8.51277e13i | 0.771625i | ||||||||
\(220\) | 1.57176e14 | − | 1.22135e14i | 1.38627 | − | 1.07722i | ||||
\(221\) | 1.10961e14 | 0.952391 | ||||||||
\(222\) | − | 1.48390e14i | − | 1.23962i | ||||||
\(223\) | 8.59256e13 | 0.698704 | 0.349352 | − | 0.936992i | \(-0.386402\pi\) | ||||
0.349352 | + | 0.936992i | \(0.386402\pi\) | |||||||
\(224\) | 1.99939e13 | 0.158274 | ||||||||
\(225\) | −5.03271e13 | −0.387888 | ||||||||
\(226\) | 3.26338e14i | 2.44916i | ||||||||
\(227\) | − | 1.51492e14i | − | 1.10722i | −0.832775 | − | 0.553611i | \(-0.813250\pi\) | ||
0.832775 | − | 0.553611i | \(-0.186750\pi\) | |||||||
\(228\) | − | 3.49185e14i | − | 2.48568i | ||||||
\(229\) | −9.76230e13 | −0.676923 | −0.338462 | − | 0.940980i | \(-0.609907\pi\) | ||||
−0.338462 | + | 0.940980i | \(0.609907\pi\) | |||||||
\(230\) | − | 2.56004e14i | − | 1.72934i | ||||||
\(231\) | 1.79319e14 | + | 2.30766e14i | 1.18019 | + | 1.51880i | ||||
\(232\) | 3.93790e14 | 2.52544 | ||||||||
\(233\) | 9.85499e13i | 0.615915i | 0.951400 | + | 0.307957i | \(0.0996454\pi\) | ||||
−0.951400 | + | 0.307957i | \(0.900355\pi\) | |||||||
\(234\) | −3.73288e14 | −2.27378 | ||||||||
\(235\) | −3.19940e13 | −0.189960 | ||||||||
\(236\) | −3.58879e14 | −2.07719 | ||||||||
\(237\) | 1.21128e14i | 0.683524i | ||||||||
\(238\) | − | 4.96755e14i | − | 2.73326i | ||||||
\(239\) | 2.59108e14i | 1.39025i | 0.718887 | + | 0.695127i | \(0.244652\pi\) | ||||
−0.718887 | + | 0.695127i | \(0.755348\pi\) | |||||||
\(240\) | 2.58912e14 | 1.35483 | ||||||||
\(241\) | − | 1.61570e14i | − | 0.824630i | −0.911041 | − | 0.412315i | \(-0.864720\pi\) | ||
0.911041 | − | 0.412315i | \(-0.135280\pi\) | |||||||
\(242\) | −3.34739e14 | − | 8.53321e13i | −1.66653 | − | 0.424835i | ||||
\(243\) | −1.40303e13 | −0.0681444 | ||||||||
\(244\) | 1.76945e13i | 0.0838494i | ||||||||
\(245\) | −4.68250e13 | −0.216512 | ||||||||
\(246\) | 7.89641e14 | 3.56303 | ||||||||
\(247\) | 1.11514e14 | 0.491073 | ||||||||
\(248\) | 1.10869e14i | 0.476540i | ||||||||
\(249\) | − | 4.00092e14i | − | 1.67866i | ||||||
\(250\) | 4.50272e14i | 1.84431i | ||||||||
\(251\) | 4.78963e14 | 1.91540 | 0.957701 | − | 0.287765i | \(-0.0929123\pi\) | ||||
0.957701 | + | 0.287765i | \(0.0929123\pi\) | |||||||
\(252\) | 1.10616e15i | 4.31931i | ||||||||
\(253\) | −2.32212e14 | + | 1.80442e14i | −0.885443 | + | 0.688042i | ||||
\(254\) | 3.31689e13 | 0.123518 | ||||||||
\(255\) | 6.07073e14i | 2.20800i | ||||||||
\(256\) | −5.48174e14 | −1.94751 | ||||||||
\(257\) | −2.46569e14 | −0.855735 | −0.427868 | − | 0.903841i | \(-0.640735\pi\) | ||||
−0.427868 | + | 0.903841i | \(0.640735\pi\) | |||||||
\(258\) | 4.77213e14 | 1.61806 | ||||||||
\(259\) | − | 1.40428e14i | − | 0.465215i | ||||||
\(260\) | 3.62119e14i | 1.17223i | ||||||||
\(261\) | − | 9.59606e14i | − | 3.03564i | ||||||
\(262\) | −5.13205e14 | −1.58666 | ||||||||
\(263\) | − | 2.34055e14i | − | 0.707267i | −0.935384 | − | 0.353633i | \(-0.884946\pi\) | ||
0.935384 | − | 0.353633i | \(-0.115054\pi\) | |||||||
\(264\) | −5.90715e14 | − | 7.60193e14i | −1.74484 | − | 2.24543i | ||||
\(265\) | 8.93046e13 | 0.257869 | ||||||||
\(266\) | − | 4.99231e14i | − | 1.40933i | ||||||
\(267\) | 1.76891e14 | 0.488245 | ||||||||
\(268\) | 2.78249e14 | 0.750973 | ||||||||
\(269\) | 6.99111e14 | 1.84515 | 0.922577 | − | 0.385813i | \(-0.126079\pi\) | ||||
0.922577 | + | 0.385813i | \(0.126079\pi\) | |||||||
\(270\) | − | 1.01086e15i | − | 2.60921i | ||||||
\(271\) | − | 9.74724e13i | − | 0.246074i | −0.992402 | − | 0.123037i | \(-0.960737\pi\) | ||
0.992402 | − | 0.123037i | \(-0.0392634\pi\) | |||||||
\(272\) | 5.05545e14i | 1.24838i | ||||||||
\(273\) | −5.31664e14 | −1.28429 | ||||||||
\(274\) | 2.17760e14i | 0.514607i | ||||||||
\(275\) | 6.69030e13 | − | 5.19876e13i | 0.154685 | − | 0.120200i | ||||
\(276\) | −1.67524e15 | −3.78985 | ||||||||
\(277\) | 8.35950e14i | 1.85055i | 0.379293 | + | 0.925277i | \(0.376167\pi\) | ||||
−0.379293 | + | 0.925277i | \(0.623833\pi\) | |||||||
\(278\) | 2.66790e14 | 0.577963 | ||||||||
\(279\) | 2.70171e14 | 0.572813 | ||||||||
\(280\) | 7.93111e14 | 1.64583 | ||||||||
\(281\) | − | 8.06155e14i | − | 1.63750i | −0.574152 | − | 0.818749i | \(-0.694668\pi\) | ||
0.574152 | − | 0.818749i | \(-0.305332\pi\) | |||||||
\(282\) | 3.16299e14i | 0.628931i | ||||||||
\(283\) | 5.16133e14i | 1.00472i | 0.864660 | + | 0.502358i | \(0.167534\pi\) | ||||
−0.864660 | + | 0.502358i | \(0.832466\pi\) | |||||||
\(284\) | 1.09911e15 | 2.09475 | ||||||||
\(285\) | 6.10099e14i | 1.13849i | ||||||||
\(286\) | 4.96235e14 | − | 3.85604e14i | 0.906758 | − | 0.704605i | ||||
\(287\) | 7.47269e14 | 1.33717 | ||||||||
\(288\) | 1.60501e14i | 0.281270i | ||||||||
\(289\) | −6.02734e14 | −1.03452 | ||||||||
\(290\) | −1.40637e15 | −2.36435 | ||||||||
\(291\) | −1.56533e15 | −2.57779 | ||||||||
\(292\) | − | 5.42453e14i | − | 0.875114i | ||||||
\(293\) | − | 7.70227e14i | − | 1.21734i | −0.793422 | − | 0.608671i | \(-0.791703\pi\) | ||
0.793422 | − | 0.608671i | \(-0.208297\pi\) | |||||||
\(294\) | 4.62922e14i | 0.716842i | ||||||||
\(295\) | 6.27036e14 | 0.951394 | ||||||||
\(296\) | 4.62599e14i | 0.687788i | ||||||||
\(297\) | −9.16913e14 | + | 7.12496e14i | −1.33595 | + | 1.03811i | ||||
\(298\) | −9.10283e14 | −1.29981 | ||||||||
\(299\) | − | 5.34995e14i | − | 0.748726i | ||||||
\(300\) | 4.82657e14 | 0.662081 | ||||||||
\(301\) | 4.51606e14 | 0.607240 | ||||||||
\(302\) | 5.09176e14 | 0.671160 | ||||||||
\(303\) | 2.09501e15i | 2.70726i | ||||||||
\(304\) | 5.08065e14i | 0.643691i | ||||||||
\(305\) | − | 3.09161e13i | − | 0.0384048i | ||||||
\(306\) | 3.98771e15 | 4.85731 | ||||||||
\(307\) | − | 7.09071e14i | − | 0.846954i | −0.905907 | − | 0.423477i | \(-0.860810\pi\) | ||
0.905907 | − | 0.423477i | \(-0.139190\pi\) | |||||||
\(308\) | −1.14266e15 | − | 1.47049e15i | −1.33848 | − | 1.72249i | ||||
\(309\) | −1.33484e15 | −1.53348 | ||||||||
\(310\) | − | 3.95954e14i | − | 0.446144i | ||||||
\(311\) | 9.38277e14 | 1.03698 | 0.518488 | − | 0.855085i | \(-0.326495\pi\) | ||||
0.518488 | + | 0.855085i | \(0.326495\pi\) | |||||||
\(312\) | 1.75142e15 | 1.89873 | ||||||||
\(313\) | 6.13649e14 | 0.652611 | 0.326305 | − | 0.945264i | \(-0.394196\pi\) | ||||
0.326305 | + | 0.945264i | \(0.394196\pi\) | |||||||
\(314\) | 2.20864e15i | 2.30434i | ||||||||
\(315\) | − | 1.93269e15i | − | 1.97833i | ||||||
\(316\) | − | 7.71853e14i | − | 0.775197i | ||||||
\(317\) | −4.79474e14 | −0.472509 | −0.236254 | − | 0.971691i | \(-0.575920\pi\) | ||||
−0.236254 | + | 0.971691i | \(0.575920\pi\) | |||||||
\(318\) | − | 8.82884e14i | − | 0.853770i | ||||||
\(319\) | 9.91268e14 | + | 1.27567e15i | 0.940691 | + | 1.21058i | ||||
\(320\) | 1.07792e15 | 1.00389 | ||||||||
\(321\) | − | 6.89204e14i | − | 0.629967i | ||||||
\(322\) | −2.39510e15 | −2.14876 | ||||||||
\(323\) | −1.19126e15 | −1.04904 | ||||||||
\(324\) | −2.13030e15 | −1.84150 | ||||||||
\(325\) | 1.54139e14i | 0.130801i | ||||||||
\(326\) | 2.67207e14i | 0.222609i | ||||||||
\(327\) | − | 1.64745e15i | − | 1.34749i | ||||||
\(328\) | −2.46167e15 | −1.97691 | ||||||||
\(329\) | 2.99326e14i | 0.236031i | ||||||||
\(330\) | 2.10967e15 | + | 2.71494e15i | 1.63354 | + | 2.10221i | ||||
\(331\) | −1.69210e15 | −1.28665 | −0.643323 | − | 0.765595i | \(-0.722445\pi\) | ||||
−0.643323 | + | 0.765595i | \(0.722445\pi\) | |||||||
\(332\) | 2.54947e15i | 1.90380i | ||||||||
\(333\) | 1.12729e15 | 0.826739 | ||||||||
\(334\) | 5.46519e14 | 0.393664 | ||||||||
\(335\) | −4.86159e14 | −0.343961 | ||||||||
\(336\) | − | 2.42230e15i | − | 1.68342i | ||||||
\(337\) | 2.53387e14i | 0.172983i | 0.996253 | + | 0.0864917i | \(0.0275656\pi\) | ||||
−0.996253 | + | 0.0864917i | \(0.972434\pi\) | |||||||
\(338\) | − | 1.42112e15i | − | 0.953079i | ||||||
\(339\) | −3.73115e15 | −2.45835 | ||||||||
\(340\) | − | 3.86840e15i | − | 2.50414i | ||||||
\(341\) | −3.59155e14 | + | 2.79085e14i | −0.228431 | + | 0.177505i | ||||
\(342\) | 4.00759e15 | 2.50453 | ||||||||
\(343\) | − | 1.37630e15i | − | 0.845180i | ||||||
\(344\) | −1.48769e15 | −0.897763 | ||||||||
\(345\) | 2.92700e15 | 1.73583 | ||||||||
\(346\) | −3.96012e15 | −2.30808 | ||||||||
\(347\) | 2.04744e15i | 1.17283i | 0.810012 | + | 0.586413i | \(0.199460\pi\) | ||||
−0.810012 | + | 0.586413i | \(0.800540\pi\) | |||||||
\(348\) | 9.20301e15i | 5.18149i | ||||||||
\(349\) | − | 2.25596e14i | − | 0.124847i | −0.998050 | − | 0.0624235i | \(-0.980117\pi\) | ||
0.998050 | − | 0.0624235i | \(-0.0198830\pi\) | |||||||
\(350\) | 6.90057e14 | 0.375385 | ||||||||
\(351\) | − | 2.11249e15i | − | 1.12967i | ||||||
\(352\) | −1.65797e14 | − | 2.13364e14i | −0.0871606 | − | 0.112167i | ||||
\(353\) | 2.52674e15 | 1.30591 | 0.652953 | − | 0.757398i | \(-0.273530\pi\) | ||||
0.652953 | + | 0.757398i | \(0.273530\pi\) | |||||||
\(354\) | − | 6.19901e15i | − | 3.14994i | ||||||
\(355\) | −1.92038e15 | −0.959439 | ||||||||
\(356\) | −1.12719e15 | −0.553727 | ||||||||
\(357\) | 5.67960e15 | 2.74352 | ||||||||
\(358\) | − | 6.00749e15i | − | 2.85361i | ||||||
\(359\) | − | 5.71819e14i | − | 0.267111i | −0.991041 | − | 0.133556i | \(-0.957361\pi\) | ||
0.991041 | − | 0.133556i | \(-0.0426395\pi\) | |||||||
\(360\) | 6.36672e15i | 2.92483i | ||||||||
\(361\) | 1.01611e15 | 0.459091 | ||||||||
\(362\) | 3.21514e15i | 1.42872i | ||||||||
\(363\) | 9.75636e14 | − | 3.82720e15i | 0.426430 | − | 1.67279i | ||||
\(364\) | 3.38788e15 | 1.45653 | ||||||||
\(365\) | 9.47778e14i | 0.400820i | ||||||||
\(366\) | −3.05642e14 | −0.127153 | ||||||||
\(367\) | 2.80841e15 | 1.14938 | 0.574692 | − | 0.818370i | \(-0.305122\pi\) | ||||
0.574692 | + | 0.818370i | \(0.305122\pi\) | |||||||
\(368\) | 2.43748e15 | 0.981418 | ||||||||
\(369\) | 5.99872e15i | 2.37630i | ||||||||
\(370\) | − | 1.65212e15i | − | 0.643918i | ||||||
\(371\) | − | 8.35508e14i | − | 0.320411i | ||||||
\(372\) | −2.59105e15 | −0.977727 | ||||||||
\(373\) | 2.07457e15i | 0.770327i | 0.922848 | + | 0.385163i | \(0.125855\pi\) | ||||
−0.922848 | + | 0.385163i | \(0.874145\pi\) | |||||||
\(374\) | −5.30112e15 | + | 4.11929e15i | −1.93704 | + | 1.50519i | ||||
\(375\) | −5.14814e15 | −1.85124 | ||||||||
\(376\) | − | 9.86048e14i | − | 0.348956i | ||||||
\(377\) | −2.93902e15 | −1.02366 | ||||||||
\(378\) | −9.45731e15 | −3.24203 | ||||||||
\(379\) | 4.00294e15 | 1.35065 | 0.675326 | − | 0.737519i | \(-0.264003\pi\) | ||||
0.675326 | + | 0.737519i | \(0.264003\pi\) | |||||||
\(380\) | − | 3.88768e15i | − | 1.29119i | ||||||
\(381\) | 3.79233e14i | 0.123981i | ||||||||
\(382\) | 5.26677e15i | 1.69498i | ||||||||
\(383\) | 2.55436e13 | 0.00809261 | 0.00404631 | − | 0.999992i | \(-0.498712\pi\) | ||||
0.00404631 | + | 0.999992i | \(0.498712\pi\) | |||||||
\(384\) | − | 9.87034e15i | − | 3.07854i | ||||||
\(385\) | 1.99646e15 | + | 2.56925e15i | 0.613051 | + | 0.788937i | ||||
\(386\) | 1.10243e16 | 3.33293 | ||||||||
\(387\) | 3.62528e15i | 1.07913i | ||||||||
\(388\) | 9.97463e15 | 2.92352 | ||||||||
\(389\) | −3.61597e15 | −1.04358 | −0.521792 | − | 0.853073i | \(-0.674736\pi\) | ||||
−0.521792 | + | 0.853073i | \(0.674736\pi\) | |||||||
\(390\) | −6.25498e15 | −1.77762 | ||||||||
\(391\) | 5.71518e15i | 1.59945i | ||||||||
\(392\) | − | 1.44314e15i | − | 0.397732i | ||||||
\(393\) | − | 5.86768e15i | − | 1.59262i | ||||||
\(394\) | −1.01749e16 | −2.71989 | ||||||||
\(395\) | 1.34859e15i | 0.355056i | ||||||||
\(396\) | 1.18044e16 | − | 9.17271e15i | 3.06106 | − | 2.37863i | ||||
\(397\) | −4.69951e15 | −1.20035 | −0.600177 | − | 0.799867i | \(-0.704903\pi\) | ||||
−0.600177 | + | 0.799867i | \(0.704903\pi\) | |||||||
\(398\) | 8.41736e14i | 0.211776i | ||||||||
\(399\) | 5.70791e15 | 1.41462 | ||||||||
\(400\) | −7.02267e14 | −0.171452 | ||||||||
\(401\) | −6.15145e15 | −1.47949 | −0.739744 | − | 0.672889i | \(-0.765053\pi\) | ||||
−0.739744 | + | 0.672889i | \(0.765053\pi\) | |||||||
\(402\) | 4.80627e15i | 1.13881i | ||||||||
\(403\) | − | 8.27462e14i | − | 0.193160i | ||||||
\(404\) | − | 1.33499e16i | − | 3.07036i | ||||||
\(405\) | 3.72208e15 | 0.843444 | ||||||||
\(406\) | 1.31576e16i | 2.93779i | ||||||||
\(407\) | −1.49857e15 | + | 1.16448e15i | −0.329694 | + | 0.256192i | ||||
\(408\) | −1.87099e16 | −4.05611 | ||||||||
\(409\) | − | 4.23567e15i | − | 0.904861i | −0.891800 | − | 0.452431i | \(-0.850557\pi\) | ||
0.891800 | − | 0.452431i | \(-0.149443\pi\) | |||||||
\(410\) | 8.79155e15 | 1.85081 | ||||||||
\(411\) | −2.48974e15 | −0.516539 | ||||||||
\(412\) | 8.50587e15 | 1.73914 | ||||||||
\(413\) | − | 5.86637e15i | − | 1.18214i | ||||||
\(414\) | − | 1.92267e16i | − | 3.81859i | ||||||
\(415\) | − | 4.45446e15i | − | 0.871981i | ||||||
\(416\) | 4.91573e14 | 0.0948480 | ||||||||
\(417\) | 3.05031e15i | 0.580133i | ||||||||
\(418\) | −5.32755e15 | + | 4.13982e15i | −0.998779 | + | 0.776111i | ||||
\(419\) | −1.99763e15 | −0.369174 | −0.184587 | − | 0.982816i | \(-0.559095\pi\) | ||||
−0.184587 | + | 0.982816i | \(0.559095\pi\) | |||||||
\(420\) | 1.85353e16i | 3.37679i | ||||||||
\(421\) | 7.56290e14 | 0.135830 | 0.0679150 | − | 0.997691i | \(-0.478365\pi\) | ||||
0.0679150 | + | 0.997691i | \(0.478365\pi\) | |||||||
\(422\) | 8.08912e14 | 0.143227 | ||||||||
\(423\) | −2.40285e15 | −0.419454 | ||||||||
\(424\) | 2.75235e15i | 0.473706i | ||||||||
\(425\) | − | 1.64661e15i | − | 0.279420i | ||||||
\(426\) | 1.89853e16i | 3.17658i | ||||||||
\(427\) | −2.89242e14 | −0.0477192 | ||||||||
\(428\) | 4.39176e15i | 0.714457i | ||||||||
\(429\) | 4.40877e15 | + | 5.67365e15i | 0.707250 | + | 0.910163i | ||||
\(430\) | 5.31310e15 | 0.840499 | ||||||||
\(431\) | 6.40123e15i | 0.998618i | 0.866424 | + | 0.499309i | \(0.166413\pi\) | ||||
−0.866424 | + | 0.499309i | \(0.833587\pi\) | |||||||
\(432\) | 9.62465e15 | 1.48075 | ||||||||
\(433\) | 4.99072e15 | 0.757244 | 0.378622 | − | 0.925551i | \(-0.376398\pi\) | ||||
0.378622 | + | 0.925551i | \(0.376398\pi\) | |||||||
\(434\) | −3.70443e15 | −0.554349 | ||||||||
\(435\) | − | 1.60796e16i | − | 2.37323i | ||||||
\(436\) | 1.04979e16i | 1.52821i | ||||||||
\(437\) | 5.74367e15i | 0.824710i | ||||||||
\(438\) | 9.36993e15 | 1.32706 | ||||||||
\(439\) | 3.14598e15i | 0.439511i | 0.975555 | + | 0.219755i | \(0.0705259\pi\) | ||||
−0.975555 | + | 0.219755i | \(0.929474\pi\) | |||||||
\(440\) | −6.57679e15 | − | 8.46369e15i | −0.906354 | − | 1.16639i | ||||
\(441\) | −3.51671e15 | −0.478084 | ||||||||
\(442\) | − | 1.22133e16i | − | 1.63795i | ||||||
\(443\) | 9.12607e15 | 1.20743 | 0.603715 | − | 0.797201i | \(-0.293687\pi\) | ||||
0.603715 | + | 0.797201i | \(0.293687\pi\) | |||||||
\(444\) | −1.08111e16 | −1.41115 | ||||||||
\(445\) | 1.96943e15 | 0.253618 | ||||||||
\(446\) | − | 9.45775e15i | − | 1.20165i | ||||||
\(447\) | − | 1.04076e16i | − | 1.30469i | ||||||
\(448\) | − | 1.00847e16i | − | 1.24737i | ||||||
\(449\) | 2.52097e15 | 0.307673 | 0.153836 | − | 0.988096i | \(-0.450837\pi\) | ||||
0.153836 | + | 0.988096i | \(0.450837\pi\) | |||||||
\(450\) | 5.53945e15i | 0.667101i | ||||||||
\(451\) | −6.19665e15 | − | 7.97448e15i | −0.736372 | − | 0.947640i | ||||
\(452\) | 2.37757e16 | 2.78806 | ||||||||
\(453\) | 5.82161e15i | 0.673680i | ||||||||
\(454\) | −1.66746e16 | −1.90423 | ||||||||
\(455\) | −5.91934e15 | −0.667121 | ||||||||
\(456\) | −1.88031e16 | −2.09142 | ||||||||
\(457\) | − | 7.50373e15i | − | 0.823721i | −0.911247 | − | 0.411861i | \(-0.864879\pi\) | ||
0.911247 | − | 0.411861i | \(-0.135121\pi\) | |||||||
\(458\) | 1.07453e16i | 1.16419i | ||||||||
\(459\) | 2.25670e16i | 2.41323i | ||||||||
\(460\) | −1.86515e16 | −1.96864 | ||||||||
\(461\) | − | 1.10124e16i | − | 1.14730i | −0.819099 | − | 0.573651i | \(-0.805526\pi\) | ||
0.819099 | − | 0.573651i | \(-0.194474\pi\) | |||||||
\(462\) | 2.54002e16 | − | 1.97374e16i | 2.61207 | − | 2.02973i | ||||
\(463\) | 4.64255e15 | 0.471271 | 0.235635 | − | 0.971842i | \(-0.424283\pi\) | ||||
0.235635 | + | 0.971842i | \(0.424283\pi\) | |||||||
\(464\) | − | 1.33904e16i | − | 1.34179i | ||||||
\(465\) | 4.52710e15 | 0.447819 | ||||||||
\(466\) | 1.08473e16 | 1.05927 | ||||||||
\(467\) | 2.10486e15 | 0.202918 | 0.101459 | − | 0.994840i | \(-0.467649\pi\) | ||||
0.101459 | + | 0.994840i | \(0.467649\pi\) | |||||||
\(468\) | 2.71963e16i | 2.58842i | ||||||||
\(469\) | 4.54836e15i | 0.427384i | ||||||||
\(470\) | 3.52155e15i | 0.326698i | ||||||||
\(471\) | −2.52522e16 | −2.31299 | ||||||||
\(472\) | 1.93251e16i | 1.74771i | ||||||||
\(473\) | −3.74489e15 | − | 4.81931e15i | −0.334405 | − | 0.430346i | ||||
\(474\) | 1.33324e16 | 1.17554 | ||||||||
\(475\) | − | 1.65482e15i | − | 0.144075i | ||||||
\(476\) | −3.61916e16 | −3.11148 | ||||||||
\(477\) | 6.70706e15 | 0.569406 | ||||||||
\(478\) | 2.85198e16 | 2.39100 | ||||||||
\(479\) | − | 6.36757e15i | − | 0.527182i | −0.964635 | − | 0.263591i | \(-0.915093\pi\) | ||
0.964635 | − | 0.263591i | \(-0.0849069\pi\) | |||||||
\(480\) | 2.68943e15i | 0.219894i | ||||||||
\(481\) | − | 3.45258e15i | − | 0.278788i | ||||||
\(482\) | −1.77839e16 | −1.41822 | ||||||||
\(483\) | − | 2.73841e16i | − | 2.15683i | ||||||
\(484\) | −6.21696e15 | + | 2.43877e16i | −0.483622 | + | 1.89714i | ||||
\(485\) | −1.74278e16 | −1.33903 | ||||||||
\(486\) | 1.54431e15i | 0.117197i | ||||||||
\(487\) | 1.41180e15 | 0.105828 | 0.0529140 | − | 0.998599i | \(-0.483149\pi\) | ||||
0.0529140 | + | 0.998599i | \(0.483149\pi\) | |||||||
\(488\) | 9.52826e14 | 0.0705496 | ||||||||
\(489\) | −3.05509e15 | −0.223445 | ||||||||
\(490\) | 5.15398e15i | 0.372363i | ||||||||
\(491\) | 1.81589e16i | 1.29599i | 0.761645 | + | 0.647995i | \(0.224392\pi\) | ||||
−0.761645 | + | 0.647995i | \(0.775608\pi\) | |||||||
\(492\) | − | 5.75302e16i | − | 4.05607i | ||||||
\(493\) | 3.13966e16 | 2.18676 | ||||||||
\(494\) | − | 1.22742e16i | − | 0.844562i | ||||||
\(495\) | −2.06247e16 | + | 1.60266e16i | −1.40203 | + | 1.08946i | ||||
\(496\) | 3.76998e15 | 0.253191 | ||||||||
\(497\) | 1.79665e16i | 1.19214i | ||||||||
\(498\) | −4.40377e16 | −2.88701 | ||||||||
\(499\) | −8.80426e11 | −5.70282e−5 | −2.85141e−5 | − | 1.00000i | \(-0.500009\pi\) | ||||
−2.85141e−5 | 1.00000i | \(0.500009\pi\) | ||||||||
\(500\) | 3.28050e16 | 2.09952 | ||||||||
\(501\) | 6.24856e15i | 0.395142i | ||||||||
\(502\) | − | 5.27190e16i | − | 3.29416i | ||||||
\(503\) | − | 2.23972e15i | − | 0.138289i | −0.997607 | − | 0.0691443i | \(-0.977973\pi\) | ||
0.997607 | − | 0.0691443i | \(-0.0220269\pi\) | |||||||
\(504\) | 5.95652e16 | 3.63420 | ||||||||
\(505\) | 2.33250e16i | 1.40629i | ||||||||
\(506\) | 1.98611e16 | + | 2.55593e16i | 1.18331 | + | 1.52281i | ||||
\(507\) | 1.62482e16 | 0.956658 | ||||||||
\(508\) | − | 2.41656e15i | − | 0.140610i | ||||||
\(509\) | −1.11422e16 | −0.640715 | −0.320358 | − | 0.947297i | \(-0.603803\pi\) | ||||
−0.320358 | + | 0.947297i | \(0.603803\pi\) | |||||||
\(510\) | 6.68199e16 | 3.79739 | ||||||||
\(511\) | 8.86714e15 | 0.498033 | ||||||||
\(512\) | 2.82114e16i | 1.56605i | ||||||||
\(513\) | 2.26795e16i | 1.24431i | ||||||||
\(514\) | 2.71396e16i | 1.47172i | ||||||||
\(515\) | −1.48615e16 | −0.796563 | ||||||||
\(516\) | − | 3.47679e16i | − | 1.84196i | ||||||
\(517\) | 3.19426e15 | − | 2.48213e15i | 0.167274 | − | 0.129981i | ||||
\(518\) | −1.54567e16 | −0.800090 | ||||||||
\(519\) | − | 4.52776e16i | − | 2.31675i | ||||||
\(520\) | 1.94996e16 | 0.986292 | ||||||||
\(521\) | −3.10384e16 | −1.55193 | −0.775966 | − | 0.630775i | \(-0.782737\pi\) | ||||
−0.775966 | + | 0.630775i | \(0.782737\pi\) | |||||||
\(522\) | −1.05623e17 | −5.22078 | ||||||||
\(523\) | 1.49526e16i | 0.730648i | 0.930881 | + | 0.365324i | \(0.119042\pi\) | ||||
−0.930881 | + | 0.365324i | \(0.880958\pi\) | |||||||
\(524\) | 3.73901e16i | 1.80621i | ||||||||
\(525\) | 7.88969e15i | 0.376794i | ||||||||
\(526\) | −2.57622e16 | −1.21638 | ||||||||
\(527\) | 8.83951e15i | 0.412634i | ||||||||
\(528\) | −2.58496e16 | + | 2.00867e16i | −1.19303 | + | 0.927053i | ||||
\(529\) | 5.64108e15 | 0.257412 | ||||||||
\(530\) | − | 9.82968e15i | − | 0.443490i | ||||||
\(531\) | 4.70924e16 | 2.10080 | ||||||||
\(532\) | −3.63720e16 | −1.60434 | ||||||||
\(533\) | 1.83725e16 | 0.801319 | ||||||||
\(534\) | − | 1.94702e16i | − | 0.839697i | ||||||
\(535\) | − | 7.67332e15i | − | 0.327236i | ||||||
\(536\) | − | 1.49833e16i | − | 0.631858i | ||||||
\(537\) | 6.86860e16 | 2.86433 | ||||||||
\(538\) | − | 7.69505e16i | − | 3.17335i | ||||||
\(539\) | 4.67498e15 | − | 3.63274e15i | 0.190655 | − | 0.148150i | ||||
\(540\) | −7.36473e16 | −2.97026 | ||||||||
\(541\) | − | 3.60531e16i | − | 1.43800i | −0.695009 | − | 0.719001i | \(-0.744600\pi\) | ||
0.695009 | − | 0.719001i | \(-0.255400\pi\) | |||||||
\(542\) | −1.07287e16 | −0.423205 | ||||||||
\(543\) | −3.67599e16 | −1.43409 | ||||||||
\(544\) | −5.25132e15 | −0.202617 | ||||||||
\(545\) | − | 1.83421e16i | − | 0.699953i | ||||||
\(546\) | 5.85198e16i | 2.20875i | ||||||||
\(547\) | 4.36538e16i | 1.62966i | 0.579698 | + | 0.814831i | \(0.303170\pi\) | ||||
−0.579698 | + | 0.814831i | \(0.696830\pi\) | |||||||
\(548\) | 1.58652e16 | 0.585816 | ||||||||
\(549\) | − | 2.32189e15i | − | 0.0848024i | ||||||
\(550\) | −5.72222e15 | − | 7.36395e15i | −0.206723 | − | 0.266032i | ||||
\(551\) | 3.15531e16 | 1.12754 | ||||||||
\(552\) | 9.02094e16i | 3.18873i | ||||||||
\(553\) | 1.26170e16 | 0.441170 | ||||||||
\(554\) | 9.20122e16 | 3.18264 | ||||||||
\(555\) | 1.88893e16 | 0.646335 | ||||||||
\(556\) | − | 1.94372e16i | − | 0.657939i | ||||||
\(557\) | 5.46434e15i | 0.182981i | 0.995806 | + | 0.0914906i | \(0.0291631\pi\) | ||||
−0.995806 | + | 0.0914906i | \(0.970837\pi\) | |||||||
\(558\) | − | 2.97374e16i | − | 0.985141i | ||||||
\(559\) | 1.11033e16 | 0.363898 | ||||||||
\(560\) | − | 2.69689e16i | − | 0.874451i | ||||||
\(561\) | −4.70974e16 | − | 6.06098e16i | −1.51085 | − | 1.94431i | ||||
\(562\) | −8.87327e16 | −2.81622 | ||||||||
\(563\) | − | 2.85169e15i | − | 0.0895470i | −0.998997 | − | 0.0447735i | \(-0.985743\pi\) | ||
0.998997 | − | 0.0447735i | \(-0.0142566\pi\) | |||||||
\(564\) | 2.30443e16 | 0.715960 | ||||||||
\(565\) | −4.15411e16 | −1.27699 | ||||||||
\(566\) | 5.68103e16 | 1.72794 | ||||||||
\(567\) | − | 3.48227e16i | − | 1.04801i | ||||||
\(568\) | − | 5.91858e16i | − | 1.76249i | ||||||
\(569\) | 6.30617e15i | 0.185820i | 0.995675 | + | 0.0929099i | \(0.0296168\pi\) | ||||
−0.995675 | + | 0.0929099i | \(0.970383\pi\) | |||||||
\(570\) | 6.71530e16 | 1.95802 | ||||||||
\(571\) | 4.94247e16i | 1.42602i | 0.701151 | + | 0.713012i | \(0.252670\pi\) | ||||
−0.701151 | + | 0.713012i | \(0.747330\pi\) | |||||||
\(572\) | −2.80936e16 | − | 3.61538e16i | −0.802105 | − | 1.03223i | ||||
\(573\) | −6.02170e16 | −1.70134 | ||||||||
\(574\) | − | 8.22512e16i | − | 2.29970i | ||||||
\(575\) | −7.93913e15 | −0.219668 | ||||||||
\(576\) | 8.09554e16 | 2.21672 | ||||||||
\(577\) | −5.31904e15 | −0.144138 | −0.0720690 | − | 0.997400i | \(-0.522960\pi\) | ||||
−0.0720690 | + | 0.997400i | \(0.522960\pi\) | |||||||
\(578\) | 6.63424e16i | 1.77920i | ||||||||
\(579\) | 1.26045e17i | 3.34545i | ||||||||
\(580\) | 1.02463e17i | 2.69152i | ||||||||
\(581\) | −4.16747e16 | −1.08347 | ||||||||
\(582\) | 1.72295e17i | 4.43337i | ||||||||
\(583\) | −8.91613e15 | + | 6.92836e15i | −0.227073 | + | 0.176449i | ||||
\(584\) | −2.92103e16 | −0.736308 | ||||||||
\(585\) | − | 4.75176e16i | − | 1.18555i | ||||||
\(586\) | −8.47781e16 | −2.09362 | ||||||||
\(587\) | 6.06158e16 | 1.48169 | 0.740845 | − | 0.671676i | \(-0.234425\pi\) | ||||
0.740845 | + | 0.671676i | \(0.234425\pi\) | |||||||
\(588\) | 3.37266e16 | 0.816036 | ||||||||
\(589\) | 8.88357e15i | 0.212763i | ||||||||
\(590\) | − | 6.90173e16i | − | 1.63624i | ||||||
\(591\) | − | 1.16333e17i | − | 2.73010i | ||||||
\(592\) | 1.57302e16 | 0.365430 | ||||||||
\(593\) | − | 4.23064e16i | − | 0.972923i | −0.873702 | − | 0.486461i | \(-0.838287\pi\) | ||
0.873702 | − | 0.486461i | \(-0.161713\pi\) | |||||||
\(594\) | 7.84237e16 | + | 1.00924e17i | 1.78537 | + | 2.29760i | ||||
\(595\) | 6.32344e16 | 1.42512 | ||||||||
\(596\) | 6.63196e16i | 1.47967i | ||||||||
\(597\) | −9.62390e15 | −0.212571 | ||||||||
\(598\) | −5.88864e16 | −1.28768 | ||||||||
\(599\) | −6.95451e15 | −0.150559 | −0.0752793 | − | 0.997162i | \(-0.523985\pi\) | ||||
−0.0752793 | + | 0.997162i | \(0.523985\pi\) | |||||||
\(600\) | − | 2.59904e16i | − | 0.557065i | ||||||
\(601\) | − | 4.23344e16i | − | 0.898352i | −0.893443 | − | 0.449176i | \(-0.851718\pi\) | ||
0.893443 | − | 0.449176i | \(-0.148282\pi\) | |||||||
\(602\) | − | 4.97078e16i | − | 1.04435i | ||||||
\(603\) | −3.65121e16 | −0.759509 | ||||||||
\(604\) | − | 3.70966e16i | − | 0.764033i | ||||||
\(605\) | 1.08623e16 | − | 4.26105e16i | 0.221509 | − | 0.868929i | ||||
\(606\) | 2.30596e17 | 4.65603 | ||||||||
\(607\) | 8.57554e16i | 1.71447i | 0.514927 | + | 0.857234i | \(0.327819\pi\) | ||||
−0.514927 | + | 0.857234i | \(0.672181\pi\) | |||||||
\(608\) | −5.27749e15 | −0.104474 | ||||||||
\(609\) | −1.50436e17 | −2.94882 | ||||||||
\(610\) | −3.40290e15 | −0.0660496 | ||||||||
\(611\) | 7.35930e15i | 0.141446i | ||||||||
\(612\) | − | 2.90529e17i | − | 5.52944i | ||||||
\(613\) | 4.03048e16i | 0.759616i | 0.925065 | + | 0.379808i | \(0.124010\pi\) | ||||
−0.925065 | + | 0.379808i | \(0.875990\pi\) | |||||||
\(614\) | −7.80468e16 | −1.45662 | ||||||||
\(615\) | 1.00517e17i | 1.85776i | ||||||||
\(616\) | −7.91838e16 | + | 6.15305e16i | −1.44928 | + | 1.12618i | ||||
\(617\) | −5.94762e16 | −1.07803 | −0.539017 | − | 0.842295i | \(-0.681204\pi\) | ||||
−0.539017 | + | 0.842295i | \(0.681204\pi\) | |||||||
\(618\) | 1.46924e17i | 2.63732i | ||||||||
\(619\) | 8.45967e16 | 1.50387 | 0.751934 | − | 0.659238i | \(-0.229121\pi\) | ||||
0.751934 | + | 0.659238i | \(0.229121\pi\) | |||||||
\(620\) | −2.88477e16 | −0.507879 | ||||||||
\(621\) | 1.08807e17 | 1.89717 | ||||||||
\(622\) | − | 1.03275e17i | − | 1.78342i | ||||||
\(623\) | − | 1.84254e16i | − | 0.315129i | ||||||
\(624\) | − | 5.95552e16i | − | 1.00882i | ||||||
\(625\) | −4.56409e16 | −0.765728 | ||||||||
\(626\) | − | 6.75438e16i | − | 1.12238i | ||||||
\(627\) | −4.73322e16 | − | 6.09119e16i | −0.779025 | − | 1.00253i | ||||
\(628\) | 1.60913e17 | 2.62321 | ||||||||
\(629\) | 3.68828e16i | 0.595553i | ||||||||
\(630\) | −2.12730e17 | −3.40240 | ||||||||
\(631\) | 1.21224e17 | 1.92050 | 0.960248 | − | 0.279147i | \(-0.0900517\pi\) | ||||
0.960248 | + | 0.279147i | \(0.0900517\pi\) | |||||||
\(632\) | −4.15632e16 | −0.652239 | ||||||||
\(633\) | 9.24860e15i | 0.143765i | ||||||||
\(634\) | 5.27753e16i | 0.812634i | ||||||||
\(635\) | 4.22223e15i | 0.0644021i | ||||||||
\(636\) | −6.43235e16 | −0.971911 | ||||||||
\(637\) | 1.07708e16i | 0.161217i | ||||||||
\(638\) | 1.40411e17 | − | 1.09108e17i | 2.08199 | − | 1.61783i | ||||
\(639\) | −1.44227e17 | −2.11856 | ||||||||
\(640\) | − | 1.09892e17i | − | 1.59915i | ||||||
\(641\) | −6.98489e15 | −0.100696 | −0.0503479 | − | 0.998732i | \(-0.516033\pi\) | ||||
−0.0503479 | + | 0.998732i | \(0.516033\pi\) | |||||||
\(642\) | −7.58601e16 | −1.08344 | ||||||||
\(643\) | −8.50297e16 | −1.20311 | −0.601554 | − | 0.798832i | \(-0.705452\pi\) | ||||
−0.601554 | + | 0.798832i | \(0.705452\pi\) | |||||||
\(644\) | 1.74498e17i | 2.44610i | ||||||||
\(645\) | 6.07467e16i | 0.843655i | ||||||||
\(646\) | 1.31121e17i | 1.80417i | ||||||||
\(647\) | 4.92373e16 | 0.671225 | 0.335613 | − | 0.942000i | \(-0.391057\pi\) | ||||
0.335613 | + | 0.942000i | \(0.391057\pi\) | |||||||
\(648\) | 1.14714e17i | 1.54941i | ||||||||
\(649\) | −6.26029e16 | + | 4.86462e16i | −0.837773 | + | 0.651000i | ||||
\(650\) | 1.69659e16 | 0.224956 | ||||||||
\(651\) | − | 4.23542e16i | − | 0.556431i | ||||||
\(652\) | 1.94677e16 | 0.253413 | ||||||||
\(653\) | 1.39199e17 | 1.79539 | 0.897693 | − | 0.440622i | \(-0.145242\pi\) | ||||
0.897693 | + | 0.440622i | \(0.145242\pi\) | |||||||
\(654\) | −1.81333e17 | −2.31745 | ||||||||
\(655\) | − | 6.53284e16i | − | 0.827283i | ||||||
\(656\) | 8.37066e16i | 1.05036i | ||||||||
\(657\) | 7.11812e16i | 0.885060i | ||||||||
\(658\) | 3.29466e16 | 0.405934 | ||||||||
\(659\) | − | 6.73104e16i | − | 0.821807i | −0.911679 | − | 0.410904i | \(-0.865213\pi\) | ||
0.911679 | − | 0.410904i | \(-0.134787\pi\) | |||||||
\(660\) | 1.97800e17 | − | 1.53702e17i | 2.39310 | − | 1.85958i | ||||
\(661\) | 2.71222e16 | 0.325175 | 0.162587 | − | 0.986694i | \(-0.448016\pi\) | ||||
0.162587 | + | 0.986694i | \(0.448016\pi\) | |||||||
\(662\) | 1.86248e17i | 2.21281i | ||||||||
\(663\) | 1.39640e17 | 1.64410 | ||||||||
\(664\) | 1.37286e17 | 1.60183 | ||||||||
\(665\) | 6.35496e16 | 0.734823 | ||||||||
\(666\) | − | 1.24079e17i | − | 1.42185i | ||||||
\(667\) | − | 1.51379e17i | − | 1.71913i | ||||||
\(668\) | − | 3.98172e16i | − | 0.448138i | ||||||
\(669\) | 1.08134e17 | 1.20616 | ||||||||
\(670\) | 5.35111e16i | 0.591555i | ||||||||
\(671\) | 2.39850e15 | + | 3.08664e15i | 0.0262788 | + | 0.0338182i | ||||
\(672\) | 2.51615e16 | 0.273226 | ||||||||
\(673\) | − | 1.09308e17i | − | 1.17641i | −0.808710 | − | 0.588207i | \(-0.799834\pi\) | ||
0.808710 | − | 0.588207i | \(-0.200166\pi\) | |||||||
\(674\) | 2.78900e16 | 0.297502 | ||||||||
\(675\) | −3.13485e16 | −0.331432 | ||||||||
\(676\) | −1.03537e17 | −1.08496 | ||||||||
\(677\) | − | 1.79269e17i | − | 1.86198i | −0.365048 | − | 0.930989i | \(-0.618948\pi\) | ||
0.365048 | − | 0.930989i | \(-0.381052\pi\) | |||||||
\(678\) | 4.10684e17i | 4.22795i | ||||||||
\(679\) | 1.63049e17i | 1.66380i | ||||||||
\(680\) | −2.08308e17 | −2.10694 | ||||||||
\(681\) | − | 1.90647e17i | − | 1.91138i | ||||||
\(682\) | 3.07186e16 | + | 3.95319e16i | 0.305278 | + | 0.392863i | ||||
\(683\) | −1.51337e17 | −1.49080 | −0.745401 | − | 0.666616i | \(-0.767742\pi\) | ||||
−0.745401 | + | 0.666616i | \(0.767742\pi\) | |||||||
\(684\) | − | 2.91977e17i | − | 2.85110i | ||||||
\(685\) | −2.77198e16 | −0.268316 | ||||||||
\(686\) | −1.51488e17 | −1.45357 | ||||||||
\(687\) | −1.22855e17 | −1.16856 | ||||||||
\(688\) | 5.05874e16i | 0.476992i | ||||||||
\(689\) | − | 2.05420e16i | − | 0.192011i | ||||||
\(690\) | − | 3.22172e17i | − | 2.98533i | ||||||
\(691\) | −1.63937e16 | −0.150594 | −0.0752971 | − | 0.997161i | \(-0.523991\pi\) | ||||
−0.0752971 | + | 0.997161i | \(0.523991\pi\) | |||||||
\(692\) | 2.88519e17i | 2.62747i | ||||||||
\(693\) | 1.49941e17 | + | 1.92959e17i | 1.35369 | + | 1.74207i | ||||
\(694\) | 2.25359e17 | 2.01706 | ||||||||
\(695\) | 3.39609e16i | 0.301350i | ||||||||
\(696\) | 4.95570e17 | 4.35963 | ||||||||
\(697\) | −1.96268e17 | −1.71180 | ||||||||
\(698\) | −2.48311e16 | −0.214716 | ||||||||
\(699\) | 1.24021e17i | 1.06324i | ||||||||
\(700\) | − | 5.02749e16i | − | 0.427329i | ||||||
\(701\) | 1.01123e17i | 0.852201i | 0.904676 | + | 0.426100i | \(0.140113\pi\) | ||||
−0.904676 | + | 0.426100i | \(0.859887\pi\) | |||||||
\(702\) | −2.32520e17 | −1.94284 | ||||||||
\(703\) | 3.70667e16i | 0.307080i | ||||||||
\(704\) | −1.07619e17 | + | 8.36265e16i | −0.884003 | + | 0.686923i | ||||
\(705\) | −4.02632e16 | −0.327925 | ||||||||
\(706\) | − | 2.78116e17i | − | 2.24594i | ||||||
\(707\) | 2.18222e17 | 1.74736 | ||||||||
\(708\) | −4.51635e17 | −3.58582 | ||||||||
\(709\) | 1.91717e17 | 1.50933 | 0.754664 | − | 0.656111i | \(-0.227800\pi\) | ||||
0.754664 | + | 0.656111i | \(0.227800\pi\) | |||||||
\(710\) | 2.11375e17i | 1.65007i | ||||||||
\(711\) | 1.01283e17i | 0.784008i | ||||||||
\(712\) | 6.06974e16i | 0.465897i | ||||||||
\(713\) | 4.26196e16 | 0.324394 | ||||||||
\(714\) | − | 6.25148e17i | − | 4.71839i | ||||||
\(715\) | 4.90854e16 | + | 6.31682e16i | 0.367381 | + | 0.472783i | ||||
\(716\) | −4.37682e17 | −3.24849 | ||||||||
\(717\) | 3.26078e17i | 2.39998i | ||||||||
\(718\) | −6.29396e16 | −0.459386 | ||||||||
\(719\) | 7.63742e16 | 0.552807 | 0.276403 | − | 0.961042i | \(-0.410857\pi\) | ||||
0.276403 | + | 0.961042i | \(0.410857\pi\) | |||||||
\(720\) | 2.16494e17 | 1.55400 | ||||||||
\(721\) | 1.39040e17i | 0.989757i | ||||||||
\(722\) | − | 1.11842e17i | − | 0.789557i | ||||||
\(723\) | − | 2.03330e17i | − | 1.42355i | ||||||
\(724\) | 2.34242e17 | 1.62642 | ||||||||
\(725\) | 4.36140e16i | 0.300329i | ||||||||
\(726\) | −4.21256e17 | − | 1.07387e17i | −2.87691 | − | 0.733387i | ||||
\(727\) | −1.02417e17 | −0.693692 | −0.346846 | − | 0.937922i | \(-0.612747\pi\) | ||||
−0.346846 | + | 0.937922i | \(0.612747\pi\) | |||||||
\(728\) | − | 1.82433e17i | − | 1.22550i | ||||||
\(729\) | −1.58834e17 | −1.05823 | ||||||||
\(730\) | 1.04321e17 | 0.689342 | ||||||||
\(731\) | −1.18613e17 | −0.777368 | ||||||||
\(732\) | 2.22679e16i | 0.144748i | ||||||||
\(733\) | − | 1.22040e17i | − | 0.786827i | −0.919362 | − | 0.393414i | \(-0.871294\pi\) | ||
0.919362 | − | 0.393414i | \(-0.128706\pi\) | |||||||
\(734\) | − | 3.09120e17i | − | 1.97674i | ||||||
\(735\) | −5.89275e16 | −0.373761 | ||||||||
\(736\) | 2.53192e16i | 0.159288i | ||||||||
\(737\) | 4.85378e16 | − | 3.77168e16i | 0.302883 | − | 0.235358i | ||||
\(738\) | 6.60273e17 | 4.08682 | ||||||||
\(739\) | 8.82050e16i | 0.541535i | 0.962645 | + | 0.270768i | \(0.0872775\pi\) | ||||
−0.962645 | + | 0.270768i | \(0.912722\pi\) | |||||||
\(740\) | −1.20367e17 | −0.733021 | ||||||||
\(741\) | 1.40336e17 | 0.847733 | ||||||||
\(742\) | −9.19636e16 | −0.551052 | ||||||||
\(743\) | − | 2.60043e17i | − | 1.54566i | −0.634615 | − | 0.772828i | \(-0.718841\pi\) | ||
0.634615 | − | 0.772828i | \(-0.281159\pi\) | |||||||
\(744\) | 1.39524e17i | 0.822644i | ||||||||
\(745\) | − | 1.15874e17i | − | 0.677719i | ||||||
\(746\) | 2.28346e17 | 1.32483 | ||||||||
\(747\) | − | 3.34544e17i | − | 1.92544i | ||||||
\(748\) | 3.00115e17 | + | 3.86219e17i | 1.71348 | + | 2.20508i | ||||
\(749\) | −7.17894e16 | −0.406602 | ||||||||
\(750\) | 5.66650e17i | 3.18381i | ||||||||
\(751\) | 1.35924e17 | 0.757631 | 0.378816 | − | 0.925472i | \(-0.376331\pi\) | ||||
0.378816 | + | 0.925472i | \(0.376331\pi\) | |||||||
\(752\) | −3.35295e16 | −0.185405 | ||||||||
\(753\) | 6.02757e17 | 3.30653 | ||||||||
\(754\) | 3.23496e17i | 1.76052i | ||||||||
\(755\) | 6.48155e16i | 0.349943i | ||||||||
\(756\) | 6.89023e17i | 3.69065i | ||||||||
\(757\) | −3.20247e17 | −1.70181 | −0.850904 | − | 0.525322i | \(-0.823945\pi\) | ||||
−0.850904 | + | 0.525322i | \(0.823945\pi\) | |||||||
\(758\) | − | 4.40600e17i | − | 2.32289i | ||||||
\(759\) | −2.92230e17 | + | 2.27080e17i | −1.52853 | + | 1.18776i | ||||
\(760\) | −2.09346e17 | −1.08639 | ||||||||
\(761\) | 1.46435e16i | 0.0753940i | 0.999289 | + | 0.0376970i | \(0.0120022\pi\) | ||||
−0.999289 | + | 0.0376970i | \(0.987998\pi\) | |||||||
\(762\) | 4.17419e16 | 0.213227 | ||||||||
\(763\) | −1.71603e17 | −0.869716 | ||||||||
\(764\) | 3.83716e17 | 1.92952 | ||||||||
\(765\) | 5.07615e17i | 2.53260i | ||||||||
\(766\) | − | 2.81156e15i | − | 0.0139179i | ||||||
\(767\) | − | 1.44232e17i | − | 0.708417i | ||||||
\(768\) | −6.89857e17 | −3.36195 | ||||||||
\(769\) | 2.35445e17i | 1.13850i | 0.822165 | + | 0.569249i | \(0.192766\pi\) | ||||
−0.822165 | + | 0.569249i | \(0.807234\pi\) | |||||||
\(770\) | 2.82795e17 | − | 2.19749e17i | 1.35684 | − | 1.05434i | ||||
\(771\) | −3.10298e17 | −1.47724 | ||||||||
\(772\) | − | 8.03186e17i | − | 3.79413i | ||||||
\(773\) | −2.15485e17 | −1.01004 | −0.505022 | − | 0.863106i | \(-0.668516\pi\) | ||||
−0.505022 | + | 0.863106i | \(0.668516\pi\) | |||||||
\(774\) | 3.99031e17 | 1.85593 | ||||||||
\(775\) | −1.22792e16 | −0.0566710 | ||||||||
\(776\) | − | 5.37120e17i | − | 2.45981i | ||||||
\(777\) | − | 1.76723e17i | − | 0.803094i | ||||||
\(778\) | 3.98007e17i | 1.79479i | ||||||||
\(779\) | −1.97246e17 | −0.882640 | ||||||||
\(780\) | 4.55713e17i | 2.02360i | ||||||||
\(781\) | 1.91730e17 | − | 1.48985e17i | 0.844858 | − | 0.656505i | ||||
\(782\) | 6.29065e17 | 2.75077 | ||||||||
\(783\) | − | 5.97735e17i | − | 2.59381i | ||||||
\(784\) | −4.90724e16 | −0.211320 | ||||||||
\(785\) | −2.81148e17 | −1.20148 | ||||||||
\(786\) | −6.45850e17 | −2.73903 | ||||||||
\(787\) | − | 8.63168e16i | − | 0.363285i | −0.983365 | − | 0.181642i | \(-0.941859\pi\) | ||
0.983365 | − | 0.181642i | \(-0.0581413\pi\) | |||||||
\(788\) | 7.41300e17i | 3.09625i | ||||||||
\(789\) | − | 2.94549e17i | − | 1.22095i | ||||||
\(790\) | 1.48438e17 | 0.610636 | ||||||||
\(791\) | 3.88647e17i | 1.58670i | ||||||||
\(792\) | −4.93938e17 | − | 6.35650e17i | −2.00134 | − | 2.57553i | ||||
\(793\) | −7.11136e15 | −0.0285965 | ||||||||
\(794\) | 5.17270e17i | 2.06440i | ||||||||
\(795\) | 1.12387e17 | 0.445155 | ||||||||
\(796\) | 6.13256e16 | 0.241081 | ||||||||
\(797\) | 2.00705e17 | 0.783082 | 0.391541 | − | 0.920161i | \(-0.371942\pi\) | ||||
0.391541 | + | 0.920161i | \(0.371942\pi\) | |||||||
\(798\) | − | 6.28264e17i | − | 2.43290i | ||||||
\(799\) | − | 7.86171e16i | − | 0.302159i | ||||||
\(800\) | − | 7.29476e15i | − | 0.0278273i | ||||||
\(801\) | 1.47910e17 | 0.560020 | ||||||||
\(802\) | 6.77084e17i | 2.54446i | ||||||||
\(803\) | −7.35298e16 | − | 9.46257e16i | −0.274265 | − | 0.352952i | ||||
\(804\) | 3.50166e17 | 1.29640 | ||||||||
\(805\) | − | 3.04884e17i | − | 1.12036i | ||||||
\(806\) | −9.10780e16 | −0.332203 | ||||||||
\(807\) | 8.79805e17 | 3.18526 | ||||||||
\(808\) | −7.18872e17 | −2.58335 | ||||||||
\(809\) | − | 1.72479e17i | − | 0.615242i | −0.951509 | − | 0.307621i | \(-0.900467\pi\) | ||
0.951509 | − | 0.307621i | \(-0.0995328\pi\) | |||||||
\(810\) | − | 4.09686e17i | − | 1.45058i | ||||||
\(811\) | − | 2.80349e17i | − | 0.985311i | −0.870224 | − | 0.492655i | \(-0.836026\pi\) | ||
0.870224 | − | 0.492655i | \(-0.163974\pi\) | |||||||
\(812\) | 9.58611e17 | 3.34431 | ||||||||
\(813\) | − | 1.22665e17i | − | 0.424794i | ||||||
\(814\) | 1.28173e17 | + | 1.64946e17i | 0.440606 | + | 0.567018i | ||||
\(815\) | −3.40141e16 | −0.116068 | ||||||||
\(816\) | 6.36209e17i | 2.15506i | ||||||||
\(817\) | −1.19204e17 | −0.400828 | ||||||||
\(818\) | −4.66216e17 | −1.55621 | ||||||||
\(819\) | −4.44561e17 | −1.47309 | ||||||||
\(820\) | − | 6.40518e17i | − | 2.10692i | ||||||
\(821\) | 6.55715e16i | 0.214119i | 0.994253 | + | 0.107060i | \(0.0341436\pi\) | ||||
−0.994253 | + | 0.107060i | \(0.965856\pi\) | |||||||
\(822\) | 2.74043e17i | 0.888358i | ||||||||
\(823\) | 4.93737e17 | 1.58890 | 0.794450 | − | 0.607329i | \(-0.207759\pi\) | ||||
0.794450 | + | 0.607329i | \(0.207759\pi\) | |||||||
\(824\) | − | 4.58029e17i | − | 1.46329i | ||||||
\(825\) | 8.41949e16 | − | 6.54244e16i | 0.267031 | − | 0.207499i | ||||
\(826\) | −6.45706e17 | −2.03308 | ||||||||
\(827\) | 5.20125e17i | 1.62583i | 0.582384 | + | 0.812914i | \(0.302120\pi\) | ||||
−0.582384 | + | 0.812914i | \(0.697880\pi\) | |||||||
\(828\) | −1.40078e18 | −4.34699 | ||||||||
\(829\) | −2.96441e17 | −0.913295 | −0.456648 | − | 0.889648i | \(-0.650950\pi\) | ||||
−0.456648 | + | 0.889648i | \(0.650950\pi\) | |||||||
\(830\) | −4.90299e17 | −1.49966 | ||||||||
\(831\) | 1.05201e18i | 3.19458i | ||||||||
\(832\) | − | 2.47945e17i | − | 0.747508i | ||||||
\(833\) | − | 1.15061e17i | − | 0.344395i | ||||||
\(834\) | 3.35745e17 | 0.997729 | ||||||||
\(835\) | 6.95690e16i | 0.205256i | ||||||||
\(836\) | 3.01611e17 | + | 3.88144e17i | 0.883506 | + | 1.13699i | ||||
\(837\) | 1.68288e17 | 0.489442 | ||||||||
\(838\) | 2.19877e17i | 0.634916i | ||||||||
\(839\) | −7.21178e16 | −0.206762 | −0.103381 | − | 0.994642i | \(-0.532966\pi\) | ||||
−0.103381 | + | 0.994642i | \(0.532966\pi\) | |||||||
\(840\) | 9.98101e17 | 2.84118 | ||||||||
\(841\) | −4.77791e17 | −1.35040 | ||||||||
\(842\) | − | 8.32441e16i | − | 0.233604i | ||||||
\(843\) | − | 1.01452e18i | − | 2.82679i | ||||||
\(844\) | − | 5.89341e16i | − | 0.163047i | ||||||
\(845\) | 1.80901e17 | 0.496935 | ||||||||
\(846\) | 2.64479e17i | 0.721389i | ||||||||
\(847\) | −3.98651e17 | − | 1.01625e17i | −1.07967 | − | 0.275232i | ||||
\(848\) | 9.35908e16 | 0.251686 | ||||||||
\(849\) | 6.49534e17i | 1.73443i | ||||||||
\(850\) | −1.81241e17 | −0.480555 | ||||||||
\(851\) | 1.77830e17 | 0.468196 | ||||||||
\(852\) | 1.38319e18 | 3.61614 | ||||||||
\(853\) | 4.12454e17i | 1.07073i | 0.844619 | + | 0.535367i | \(0.179827\pi\) | ||||
−0.844619 | + | 0.535367i | \(0.820173\pi\) | |||||||
\(854\) | 3.18366e16i | 0.0820689i | ||||||||
\(855\) | 5.10146e17i | 1.30586i | ||||||||
\(856\) | 2.36490e17 | 0.601133 | ||||||||
\(857\) | 5.72289e17i | 1.44454i | 0.691609 | + | 0.722272i | \(0.256902\pi\) | ||||
−0.691609 | + | 0.722272i | \(0.743098\pi\) | |||||||
\(858\) | 6.24494e17 | − | 4.85269e17i | 1.56532 | − | 1.21635i | ||||
\(859\) | 2.16481e17 | 0.538840 | 0.269420 | − | 0.963023i | \(-0.413168\pi\) | ||||
0.269420 | + | 0.963023i | \(0.413168\pi\) | |||||||
\(860\) | − | 3.87091e17i | − | 0.956804i | ||||||
\(861\) | 9.40410e17 | 2.30833 | ||||||||
\(862\) | 7.04577e17 | 1.71745 | ||||||||
\(863\) | −1.36449e17 | −0.330298 | −0.165149 | − | 0.986269i | \(-0.552810\pi\) | ||||
−0.165149 | + | 0.986269i | \(0.552810\pi\) | |||||||
\(864\) | 9.99755e16i | 0.240332i | ||||||||
\(865\) | − | 5.04103e17i | − | 1.20343i | ||||||
\(866\) | − | 5.49324e17i | − | 1.30233i | ||||||
\(867\) | −7.58518e17 | −1.78588 | ||||||||
\(868\) | 2.69890e17i | 0.631058i | ||||||||
\(869\) | −1.04625e17 | − | 1.34642e17i | −0.242950 | − | 0.312653i | ||||
\(870\) | −1.76987e18 | −4.08155 | ||||||||
\(871\) | 1.11827e17i | 0.256117i | ||||||||
\(872\) | 5.65298e17 | 1.28582 | ||||||||
\(873\) | −1.30888e18 | −2.95675 | ||||||||
\(874\) | 6.32201e17 | 1.41836 | ||||||||
\(875\) | 5.36244e17i | 1.19485i | ||||||||
\(876\) | − | 6.82656e17i | − | 1.51070i | ||||||
\(877\) | − | 1.40385e17i | − | 0.308548i | −0.988028 | − | 0.154274i | \(-0.950696\pi\) | ||
0.988028 | − | 0.154274i | \(-0.0493039\pi\) | |||||||
\(878\) | 3.46276e17 | 0.755883 | ||||||||
\(879\) | − | 9.69302e17i | − | 2.10148i | ||||||
\(880\) | −2.87799e17 | + | 2.23637e17i | −0.619717 | + | 0.481557i | ||||
\(881\) | 5.87967e17 | 1.25747 | 0.628735 | − | 0.777620i | \(-0.283573\pi\) | ||||
0.628735 | + | 0.777620i | \(0.283573\pi\) | |||||||
\(882\) | 3.87081e17i | 0.822224i | ||||||||
\(883\) | 9.10590e16 | 0.192114 | 0.0960569 | − | 0.995376i | \(-0.469377\pi\) | ||||
0.0960569 | + | 0.995376i | \(0.469377\pi\) | |||||||
\(884\) | −8.89815e17 | −1.86460 | ||||||||
\(885\) | 7.89101e17 | 1.64238 | ||||||||
\(886\) | − | 1.00450e18i | − | 2.07657i | ||||||
\(887\) | 2.02712e17i | 0.416234i | 0.978104 | + | 0.208117i | \(0.0667336\pi\) | ||||
−0.978104 | + | 0.208117i | \(0.933266\pi\) | |||||||
\(888\) | 5.82164e17i | 1.18732i | ||||||||
\(889\) | 3.95020e16 | 0.0800218 | ||||||||
\(890\) | − | 2.16773e17i | − | 0.436180i | ||||||
\(891\) | −3.71611e17 | + | 2.88764e17i | −0.742715 | + | 0.577134i | ||||
\(892\) | −6.89054e17 | −1.36793 | ||||||||
\(893\) | − | 7.90089e16i | − | 0.155800i | ||||||
\(894\) | −1.14556e18 | −2.24384 | ||||||||
\(895\) | 7.64723e17 | 1.48787 | ||||||||
\(896\) | −1.02812e18 | −1.98699 | ||||||||
\(897\) | − | 6.73272e17i | − | 1.29252i | ||||||
\(898\) | − | 2.77480e17i | − | 0.529145i | ||||||
\(899\) | − | 2.34133e17i | − | 0.443511i | ||||||
\(900\) | 4.03583e17 | 0.759412 | ||||||||
\(901\) | 2.19443e17i | 0.410179i | ||||||||
\(902\) | −8.77744e17 | + | 6.82059e17i | −1.62978 | + | 1.26643i | ||||
\(903\) | 5.68329e17 | 1.04827 | ||||||||
\(904\) | − | 1.28029e18i | − | 2.34583i | ||||||
\(905\) | −4.09270e17 | −0.744936 | ||||||||
\(906\) | 6.40779e17 | 1.15861 | ||||||||
\(907\) | −2.28556e17 | −0.410534 | −0.205267 | − | 0.978706i | \(-0.565806\pi\) | ||||
−0.205267 | + | 0.978706i | \(0.565806\pi\) | |||||||
\(908\) | 1.21484e18i | 2.16773i | ||||||||
\(909\) | 1.75178e18i | 3.10525i | ||||||||
\(910\) | 6.51536e17i | 1.14733i | ||||||||
\(911\) | 2.86406e17 | 0.501040 | 0.250520 | − | 0.968111i | \(-0.419398\pi\) | ||||
0.250520 | + | 0.968111i | \(0.419398\pi\) | |||||||
\(912\) | 6.39381e17i | 1.11120i | ||||||||
\(913\) | 3.45583e17 | + | 4.44731e17i | 0.596660 | + | 0.767844i | ||||
\(914\) | −8.25929e17 | −1.41666 | ||||||||
\(915\) | − | 3.89067e16i | − | 0.0662976i | ||||||
\(916\) | 7.82858e17 | 1.32529 | ||||||||
\(917\) | −6.11193e17 | −1.02793 | ||||||||
\(918\) | 2.48393e18 | 4.15034 | ||||||||
\(919\) | − | 1.17692e18i | − | 1.95368i | −0.213981 | − | 0.976838i | \(-0.568643\pi\) | ||
0.213981 | − | 0.976838i | \(-0.431357\pi\) | |||||||
\(920\) | 1.00435e18i | 1.65638i | ||||||||
\(921\) | − | 8.92340e17i | − | 1.46208i | ||||||
\(922\) | −1.21213e18 | −1.97316 | ||||||||
\(923\) | 4.41729e17i | 0.714407i | ||||||||
\(924\) | −1.43799e18 | − | 1.85056e18i | −2.31060 | − | 2.97352i | ||||
\(925\) | −5.12350e16 | −0.0817931 | ||||||||
\(926\) | − | 5.11001e17i | − | 0.810505i | ||||||
\(927\) | −1.11615e18 | −1.75891 | ||||||||
\(928\) | 1.39092e17 | 0.217778 | ||||||||
\(929\) | 4.49755e16 | 0.0699651 | 0.0349826 | − | 0.999388i | \(-0.488862\pi\) | ||||
0.0349826 | + | 0.999388i | \(0.488862\pi\) | |||||||
\(930\) | − | 4.98294e17i | − | 0.770172i | ||||||
\(931\) | − | 1.15634e17i | − | 0.177577i | ||||||
\(932\) | − | 7.90291e17i | − | 1.20585i | ||||||
\(933\) | 1.18079e18 | 1.79012 | ||||||||
\(934\) | − | 2.31680e17i | − | 0.348985i | ||||||
\(935\) | −5.24364e17 | − | 6.74805e17i | −0.784807 | − | 1.00997i | ||||
\(936\) | 1.46448e18 | 2.17786 | ||||||||
\(937\) | − | 5.04699e17i | − | 0.745753i | −0.927881 | − | 0.372877i | \(-0.878371\pi\) | ||
0.927881 | − | 0.372877i | \(-0.121629\pi\) | |||||||
\(938\) | 5.00634e17 | 0.735027 | ||||||||
\(939\) | 7.72255e17 | 1.12659 | ||||||||
\(940\) | 2.56566e17 | 0.371905 | ||||||||
\(941\) | 5.22795e17i | 0.752997i | 0.926417 | + | 0.376499i | \(0.122872\pi\) | ||||
−0.926417 | + | 0.376499i | \(0.877128\pi\) | |||||||
\(942\) | 2.77949e18i | 3.97795i | ||||||||
\(943\) | 9.46303e17i | 1.34574i | ||||||||
\(944\) | 6.57131e17 | 0.928581 | ||||||||
\(945\) | − | 1.20387e18i | − | 1.69039i | ||||||
\(946\) | −5.30457e17 | + | 4.12197e17i | −0.740122 | + | 0.575119i | ||||
\(947\) | 1.34472e18 | 1.86437 | 0.932183 | − | 0.361987i | \(-0.117902\pi\) | ||||
0.932183 | + | 0.361987i | \(0.117902\pi\) | |||||||
\(948\) | − | 9.71348e17i | − | 1.33821i | ||||||
\(949\) | 2.18009e17 | 0.298454 | ||||||||
\(950\) | −1.82145e17 | −0.247785 | ||||||||
\(951\) | −6.03401e17 | −0.815685 | ||||||||
\(952\) | 1.94887e18i | 2.61795i | ||||||||
\(953\) | − | 8.71924e17i | − | 1.16392i | −0.813219 | − | 0.581958i | \(-0.802287\pi\) | ||
0.813219 | − | 0.581958i | \(-0.197713\pi\) | |||||||
\(954\) | − | 7.38240e17i | − | 0.979281i | ||||||
\(955\) | −6.70432e17 | −0.883760 | ||||||||
\(956\) | − | 2.07784e18i | − | 2.72185i | ||||||
\(957\) | 1.24747e18 | + | 1.60538e18i | 1.62390 | + | 2.08980i | ||||
\(958\) | −7.00872e17 | −0.906663 | ||||||||
\(959\) | 2.59338e17i | 0.333391i | ||||||||
\(960\) | 1.35652e18 | 1.73301 | ||||||||
\(961\) | −7.21744e17 | −0.916311 | ||||||||
\(962\) | −3.80022e17 | −0.479467 | ||||||||
\(963\) | − | 5.76291e17i | − | 0.722577i | ||||||
\(964\) | 1.29566e18i | 1.61447i | ||||||||
\(965\) | 1.40333e18i | 1.73779i | ||||||||
\(966\) | −3.01414e18 | −3.70938 | ||||||||
\(967\) | − | 6.81634e17i | − | 0.833667i | −0.908983 | − | 0.416833i | \(-0.863140\pi\) | ||
0.908983 | − | 0.416833i | \(-0.136860\pi\) | |||||||
\(968\) | 1.31325e18 | + | 3.34775e17i | 1.59622 | + | 0.406912i | ||||
\(969\) | −1.49916e18 | −1.81095 | ||||||||
\(970\) | 1.91826e18i | 2.30291i | ||||||||
\(971\) | 1.35264e18 | 1.61387 | 0.806934 | − | 0.590642i | \(-0.201125\pi\) | ||||
0.806934 | + | 0.590642i | \(0.201125\pi\) | |||||||
\(972\) | 1.12512e17 | 0.133414 | ||||||||
\(973\) | 3.17729e17 | 0.374437 | ||||||||
\(974\) | − | 1.55396e17i | − | 0.182006i | ||||||
\(975\) | 1.93978e17i | 0.225800i | ||||||||
\(976\) | − | 3.23999e16i | − | 0.0374839i | ||||||
\(977\) | 2.68381e17 | 0.308592 | 0.154296 | − | 0.988025i | \(-0.450689\pi\) | ||||
0.154296 | + | 0.988025i | \(0.450689\pi\) | |||||||
\(978\) | 3.36271e17i | 0.384287i | ||||||||
\(979\) | −1.96627e17 | + | 1.52791e17i | −0.223330 | + | 0.173540i | ||||
\(980\) | 3.75499e17 | 0.423889 | ||||||||
\(981\) | − | 1.37755e18i | − | 1.54558i | ||||||
\(982\) | 1.99874e18 | 2.22888 | ||||||||
\(983\) | −7.48803e17 | −0.829940 | −0.414970 | − | 0.909835i | \(-0.636208\pi\) | ||||
−0.414970 | + | 0.909835i | \(0.636208\pi\) | |||||||
\(984\) | −3.09792e18 | −3.41271 | ||||||||
\(985\) | − | 1.29521e18i | − | 1.41815i | ||||||
\(986\) | − | 3.45580e18i | − | 3.76086i | ||||||
\(987\) | 3.76691e17i | 0.407458i | ||||||||
\(988\) | −8.94250e17 | −0.961430 | ||||||||
\(989\) | 5.71890e17i | 0.611132i | ||||||||
\(990\) | 1.76404e18 | + | 2.27015e18i | 1.87369 | + | 2.41125i | ||||
\(991\) | −2.19759e17 | −0.232009 | −0.116004 | − | 0.993249i | \(-0.537009\pi\) | ||||
−0.116004 | + | 0.993249i | \(0.537009\pi\) | |||||||
\(992\) | 3.91605e16i | 0.0410939i | ||||||||
\(993\) | −2.12945e18 | −2.22112 | ||||||||
\(994\) | 1.97756e18 | 2.05027 | ||||||||
\(995\) | −1.07149e17 | −0.110420 | ||||||||
\(996\) | 3.20842e18i | 3.28651i | ||||||||
\(997\) | − | 1.43003e18i | − | 1.45604i | −0.685554 | − | 0.728022i | \(-0.740440\pi\) | ||
0.685554 | − | 0.728022i | \(-0.259560\pi\) | |||||||
\(998\) | 9.69076e13i | 9.80787e-5i | ||||||||
\(999\) | 7.02182e17 | 0.706409 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 11.13.b.b.10.1 | ✓ | 10 | |
3.2 | odd | 2 | 99.13.c.b.10.10 | 10 | |||
4.3 | odd | 2 | 176.13.h.c.65.2 | 10 | |||
11.10 | odd | 2 | inner | 11.13.b.b.10.10 | yes | 10 | |
33.32 | even | 2 | 99.13.c.b.10.1 | 10 | |||
44.43 | even | 2 | 176.13.h.c.65.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
11.13.b.b.10.1 | ✓ | 10 | 1.1 | even | 1 | trivial | |
11.13.b.b.10.10 | yes | 10 | 11.10 | odd | 2 | inner | |
99.13.c.b.10.1 | 10 | 33.32 | even | 2 | |||
99.13.c.b.10.10 | 10 | 3.2 | odd | 2 | |||
176.13.h.c.65.1 | 10 | 44.43 | even | 2 | |||
176.13.h.c.65.2 | 10 | 4.3 | odd | 2 |